Transcript Slide 1
IEEE-IFCS 2010, Newport Beach, CA
June 2, 2010
Blackbody radiation shifts and
magic wavelengths for atomic
clock research
Marianna Safronova1, M.G. Kozlov1,2,
Dansha Jiang1, and U.I. Safronova3
1University
of Delaware, USA
2PNPI, Gatchina, Russia
3University of Nevada, Reno, USA
Outline
• Black-body radiation shifts
• Microwave vs. Optical transitions
• BBR shift in Rb frequency standard
• How to calculate its uncertainty?
• Development of new methodology for precision
calculations of Group II-type system properties
• Polarizabilities
• Magic wavelengths
Blackbody radiation shifts
Level B
Clock
transition
Level A
T=0K
T = 300 K
DBBR
Transition frequency should be corrected to account for the
effect of the black body radiation at T=300K.
atomic clocks
black-body radiation ( BBR ) shift
Motivation:
BBR shift gives large contribution
into uncertainty budget for some of
the atomic clock schemes.
Accurate calculations are needed
to achieve ultimate precision
goals.
BBR shift and polarizability
BBR shift of atomic level can be expressed in terms of a
scalar static polarizability to a good approximation [1]:
4
D BBR
1
2 T (K )
0 (0)(831.9V / m)
(1+ )
2
300
Dynamic correction
Dynamic correction is generally small.
Multipolar corrections (M1 and E2) are suppressed by 2 [1].
Vector & tensor polarizability average
out due to the isotropic nature of field.
[1] Sergey Porsev and Andrei Derevianko, Physical Review A 74, 020502R (2006)
microWave
transitions
optical
transitions
Sr+
Cs
6s F=4
4d5/2
5s1/2
6s F=3
In lowest (second) order the
polarizabilities of ground hyperfine
6s1/2 F=4 and F=3 states are the
same.
(1)
(1)
2
DDT , DT D, T D
2
n Dv
1
3(2 jv 1) n En Ev
0
v
Therefore, the third-order
F-dependent polarizability
F (0) has to be calculated.
(1)
Lowest-order polarizability
terms
D2
term
BBR shifts for microwave transitions
Atom
Transition
Method
Ref.
b
2s (F=2 – F=1)
LCCSD[pT]
[1]
-0.5017 10-14
3s (F=2 – F=1)
39K
4s (F=2 – F=1)
87Rb 5s (F=2 – F=1)
LCCSD[pT]
LCCSD[pT]
CP
[7]
[2]
[3]
-0.5019 10-14
-1.118 10-14
-1.26(1) 10-14
LCCSD[pT]
CP
Experiment
6s (F=2 – F=1) CP
6s (F=1 – F=0) CP
MBPT3
6s (F=1 – F=0) CP
[4]
[3]
[5]
[3]
[3]
[6]
[3]
-1.710(6) 10-14
-1.70(2) 10-14
-1.710(3) 10-14
-0.245(2) 10-14
-0.0983 10-14
-0.094(5) 10-14
-0.0102(5) 10-14
7Li
23Na
133Cs
137Ba+
171Yb+
137Hg+
6s (F=3 – F=4)
[1] W.R. Johnson, U.I. Safronova, A. Derevianko, and M.S. Safronova, PRA 77, 022510 (2008)
[2] U.I. Safronova and M.S. Safronova, PRA 78, 052504 (2008)
[3] E. J. Angstmann, V.A. Dzuba, and V.V. Flambaum, PRA 74, 023405 (2006)
[4] K. Beloy, U.I. Safronova, and A. Derevianko, PRL 97, 040801 (2006)
[5] E. Simon, P. Laurent, and A. Clairon, PRA 57, 426 (1998)
[6] U.I. Safronova and M.S. Safronova, PRA 79, 022510 (2009)
[7] M. S. Safronova et al., IEEE - TUFFC 57, 94 (2010).
BBR shifts for microwave transitions
Atom
7Li
Transition
2s (F=2 – F=1)
3s (F=2 – F=1)
39K
4s (F=2 – F=1)
87Rb 5s (F=2 – F=1)
23Na
133Cs
6s (F=3 – F=4)
171Yb+
6s (F=2 – F=1)
6s (F=1 – F=0)
137Hg+
6s (F=1 – F=0)
137Ba+
Method
Ref.
LCCSD[pT]
[1]
LCCSD[pT]
LCCSD[pT]
CP
LCCSD[pT]
LCCSD[pT]
CP
Experiment
CP
CP
MBPT3
CP
[7]
[2]
[3]
Present
[4]
[3]
[5]
[3]
[3]
[6]
[3]
b
-0.5017 10-14
-0.5019 10-14
-1.118 10-14
-1.26(1) 10-14
-1.255(4) 10-14
-1.710(6) 10-14
-1.70(2) 10-14
-1.710(3) 10-14
-0.245(2) 10-14
-0.0983 10-14
-0.094(5) 10-14
-0.0102(5) 10-14
[1] W.R. Johnson, U.I. Safronova, A. Derevianko, and M.S. Safronova, PRA 77, 022510 (2008)
[2] U.I. Safronova and M.S. Safronova, PRA 78, 052504 (2008)
[3] E. J. Angstmann, V.A. Dzuba, and V.V. Flambaum, PRA 74, 023405 (2006)
[4] K. Beloy, U.I. Safronova, and A. Derevianko, PRL 97, 040801 (2006)
[5] E. Simon, P. Laurent, and A. Clairon, PRA 57, 426 (1998)
[6] U.I. Safronova and M.S. Safronova, PRA 79, 022510 (2009)
[7] M. S. Safronova et al., IEEE - TUFFC 57, 94 (2010).
BBR shift in Rb
b = -1.255(4) 10-14
Uncertainty estimate
How to determine theoretical uncertainty?
BBR shift in Rb
b = -1.255(4) 10-14
Uncertainty estimate
How to determine theoretical uncertainty?
Scalar Stark shift coefficient
4
T
4
b ( )3 0 ks
15
v0
1 (3)
ks F 2 (0) F(3)1 (0) 1.240(4) 1010 Hz/(V/m) 2
2
Third-order polarizability calcualtion
The third-order static scalar electric-dipole polarizability of
the hyperfine level F can be written as:
F(3) (0) C( jv , F , I ) 2T C R
Coefficient
Each term involves sums with two electric-dipole and one
hyperfine matrix element. The summations in these terms
range over core, valence bound and continuum states.
Electric-dipole matrix elements
T A
n 5 m
Hyperfine matrix elements
5s D mp mp D ns ns T (1) 5s
( Emp E5 s )( Ens E5 s )
Sources of uncertainties
Strategy: dominant terms (m, n=5-12) are calculated with
``best set’’ matrix elements and experimental energies.
The remaining terms are calculated in Dirac-Hartree-Fock
approximation.
Uncertainty calculation:
(1) Uncertainty of each of the157 matrix elements
contributing to dominant terms is estimated.
(2) Uncertainties in all remainders are evaluated.
157 “Best-set” matrix elements
Relativistic all-order matrix elements or experimental data
mp j D ns , m 5 12, n 5 12
ns T (1) 5s , n 5 12
mp j T (1) np j , m 5 7, n 5 7
Transition
Value
Transition
Value
Transition
Value
5s – 5p1/2
4.231(3)
5s – 6p1/2
0.325(9)
5s – 7p1/2
0.115(3)
6s – 5p1/2
4.146(27)
6s – 6p1/2
9.75(6)
6s – 7p1/2
0.993(7)
7s – 5p1/2
0.953(2)
7s – 6p1/2
9.21(2)
7s – 7p1/2
16.93(9)
8s – 5p1/2
0.502(2)
8s – 6p1/2
1.862(8)
8s – 7p1/2
16.00(2)
9s – 5p1/2
0.331(1)
9s – 6p1/2
0.936(5)
9s – 7p1/2
3.00(2)
Uncertainty of the remainders: Term T
T ()
m 5
n 6
n 6 12
m 5 12
fast convergence
n 5 m
slow
convergence
n 13 15% of the term T
DHF approximation is determined to be accurate to 4% by
comparing accurate results for main terms with DHF values.
Therefore, we adjust the DHF tail by 4%.
Entire adjustment (4%) is taken to be uncertainty in the tail.
Blackbody radiation shifts in
optical frequency standards:
(1) monovalent systems
(2) divalent systems
(3) other, more complicated systems
Ca + (4s1/2 3d5/2 )
Sr (5s1/2 4d5/2 )
+
Ba + (6s1/2 5d5/2 )
Ra + (7 s1/2 6d5/2 )
Mg, Ca, Zn, Cd, Sr, Al+, In+, Yb, Hg
( ns2 1S0 – nsnp 3P)
Hg+ (5d 106s – 5d 96s2)
Yb+ (4f 146s – 4f 136s2)
GOAL of the present project:
calculate properties of group II
atoms with precision comparable
to alkali-metal atoms
Configuration interaction +
all-order method
CI works for systems with many valence electrons
but can not accurately account for core-valence
and core-core correlations.
All-order (coupled-cluster) method can not accurately
describe valence-valence correlation for large systems
but accounts well for core-core and core-valence
correlations.
Therefore, two methods are combined to
acquire benefits from both approaches.
CI + ALL-ORDER RESULTS
Two-electron binding energies, differences with experiment
Atom
Mg
Ca
Zn
Sr
Cd
Ba
Hg
Ra
CI
CI + MBPT
1.9%
0.11%
4.1%
0.7%
8.0%
0.7%
5.2%
1.0%
9.6%
1.4%
6.4%
1.9%
11.8% 2.5%
7.3%
2.3%
CI + All-order
0.03%
0.3%
0.4 %
0.4%
0.2%
0.6%
0.5%
0.67%
Development of a configuration-interaction plus all-order method for
atomic calculations, M.S. Safronova, M. G. Kozlov, W.R. Johnson,
Dansha Jiang, Phys. Rev. A 80, 012516 (2009).
Cd, Zn, and Sr Polarizabilities,
preliminary results (a.u.)
Zn
CI
CI+MBPT
CI + All-order
4s2 1S0
46.2
39.45
39.28
4s4p 3P0
77.9
69.18
67.97
CI
CI+MBPT
CI+All-order
5s2 1S0
59.2
45.82
46.55
5s5p 3P0
91.2
76.75
76.54
Cd
Sr
CI +MBPT CI+all-order
Recomm.*
5s2 1S0
195.6
198.0
197.2(2)
5s5p 3P0
483.6
459.4
458.3(3.6)
*From expt. matrix elements, S. G. Porsev and A. Derevianko, PRA 74, 020502R (2006).
magic wavelength
Atom in state B
sees potential UB
Atom in state A
sees potential UA
Magic wavelength magic is the wavelength for
which the optical potential U experienced
by an atom is independent on its state
U ( )
Cd, Zn, Sr, and Hg magic wavelengths,
preliminary results (nm)
Sr
Present
813.45
Cd
Zn
Present
423(4)
414(5)
Hg
Present
365(5)
Expt. [1]
813.42735(40)
Theory [2]
360
[1] A. D. Ludlow et al., Science 319, 1805 (2008)
[2] H. Hachisu et al., Phys. Rev. Lett. 100, 053001 (2008)
Summary of the fractional uncertainties d/0 due to BBR shift and the fractional
error in the absolute transition frequency induced by the BBR shift uncertainty at
T = 300 K in various frequency standards.
Present
M. S. Safronova et al., IEEE - TUFFC 57, 94 (2010).
510-17
Conclusion
I. New BBR shift result for Rb frequency standard is
presented.
The new value is accurate to 0.3%.
II. Development of new method for calculating atomic
properties of divalent and more complicated systems
is reported (work in progress).
•
Improvement over best present approaches is demonstrated.
•
Preliminary results for Mg, Zn, Cd, and Sr polarizabilities are
presented.
Preliminary results for magic wavelengths in Cd, Zn, and Hg are
presented.
•